Nonlocal strain gradient theory for the magneto-electro-elastic vibration response of a porous FG-core sandwich nanoplate with piezomagnetic face sheets resting on an elastic foundation

The free vibration analysis of a nonlocal strain gradient elastic sandwich nanoplate with porous graded core and piezomagnetic face sheets is presented in this paper. The rectangular elastic sandwich nanoplate is resting on Pasternak's foundation. Porosities are distributed evenly and unevenly through the thickness of the core. The gradation of material properties having porosities is described using a modified power-law function. A nonlocal parameter and a strain gradient parameter are employed to describe both stiffness reduction and stiffness enhancement of nanoplates. The governing equations of the motion are derived from Hamilton's principle based on the first order shear deformation theory. In addition, Eringen's nonlocal strain gradient piezo-magneto-elasticity theory is used to consider nanoscale effects. The analytical solution is presented to solve seven governing equations of motion using Navier's solution. Eventually, the natural frequency is surveyed for different side length ratios, nonlocal coefficient, porosity volume fraction, and parameters of foundation numerically with even and uneven porosity distributions.